Sarnak's talk was stellar, spiked with humor or quipes that if RH would be proven to be false, no 1 million dollars
could be won (but he hinted that somebody else would probably pay the million bucks in this case),
and historical insight about how amazing Riemann was to find some small roots with paper and pencil and
that he did not formulate RH as a conjecture as he had been more interested in the prime number theorem. I was happy that
he also mentioned "statements for the person on the street"
in the form of Mertens (see Pset problem
1.3 this year
and the youtube short.)
Sarnak is optimistic that RH hold, stressed that counter examples could be very, very large as only the log log(z) of the size z at which
non-trivial roots might occur is expected to have reasonable size. He urged to look for extreme cases of L functions coming from
Maass forms, where he hinted that AI could be helpful.
P.S. the Logician Paul Cohen was mentioned prominently by Sarnak. Cohen was pessimistic about the RH to be decidable.
You can see Hugh Woodin below in the audience, I met him briefly before the talk and asked him what he thinks to be the most likely
thing for RH and he is undecided (meaning he would not root for one of the possibilities that it could be true, false or undecidable)
but pointed out that if it should be undecidable, it would be true (similarly like Goldbach but unlike
the prime twin conjecture. If the later would be undecidable, it would not necessarily be true.).
